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(D) Given:Inductive reactance $X_{L} = 31\,\Omega$Resistance $R = 8\,\Omega$Capacitive reactance $X_{C} = 25\,\Omega$The impedance $Z$ of a series $LC

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(D) Given:Inductive reactance $X_{L} = 31\,\Omega$Resistance $R = 8\,\Omega$Capacitive reactance $X_{C} = 25\,\Omega$The impedance $Z$ of a series $LCR$ circuit is given by the formula:$Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}$Substituting the given values:$Z = \sqrt{8^{2} + (31 - 25)^{2}}$$Z = \sqrt{64 + 6^{2}}$$Z = \sqrt{64 + 36}$$Z = \sqrt{100} = 10\,\Omega$The power factor of the circuit is defined as:$\cos \phi = \frac{R}{Z}$Substituting the values of $R$ and $Z$:$\cos \phi = \frac{8}{10} = 0.8$

$A$ coil of inductive reactance $31\,\Omega$ has a resistance of $8\,\Omega$. It is placed in series with a capacitor of capacitive reactance $25\,\Omega$. The combination is connected to an $A$.$C$. source of $110\,V$. The power factor of the circuit is:

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